In addition to hardware, there are several other factors which understate how efficient MIOSR can be relative to the results reported in Figure REF . The first is that MIO requires less hyperparameter tuning than other methods because we are directly tuning the sparsity and not a proxy threshold. Second, for especially difficult or large problems, one can use warm starts from heuristic methods to get good initial solutions, or reuse solutions and models from previous steps in the hyperparameter search (which also avoids reconstructing the full optimization model). Finally, much of the computational effort is dedicated toward proving optimality by improving the dual lower bound [1]}. Therefore, one could set a short timeout on the solver to get what is likely an optimal solution, but give up on the optimality guarantee if so desired.
